Find the values of e, a, b, and c.
-$$r = \frac { 24 } { 4 + 2 \sin \theta }$$
A) $\mathrm { e } = 2 , \mathrm { a } = \sqrt { 48 } , \mathrm {~b} = 8 , \mathrm { c } = 4$
B) $\mathrm { e } = 2 , \mathrm { a } = \sqrt { 48 } , \mathrm {~b} = 4 , \mathrm { c } = 8$
C) $\mathrm { e } = \frac { 1 } { 2 } , \mathrm { a } = 8 , \mathrm {~b} = \sqrt { 48 } , \mathrm { c } = 4$
D) $\mathrm { e } = \frac { 1 } { 2 } , \mathrm { a } = 4 , \mathrm {~b} = 8 , \mathrm { c } = \sqrt { 48 }$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form of a conic section, specifically an ellipse in polar coordinates, as $r = \frac{ep}{1 + e\sin\theta}$, where $e$ is the eccentricity, $p$ is the semi-latus rectum, and $\theta$ is the angle. Comparing this to the given equation, $r = \frac{24}{4 + 2\sin\theta}$, we can identify $e = \frac{1}{2}$, $p = 8$, indicating that $a$, the semi-major axis, is $8$, $b$, the semi-minor axis, is $\sqrt{48}$, and $c$, the focal distance, is $4$, following the relationships in ellipses.

Find the Values of E, A, B, and C r=244+2sin⁡θr = \frac { 24 } { 4 + 2 \sin \theta }r=4+2sinθ24​

Find the Values of E, A, B, and C $r = \frac { 24 } { 4 + 2 \sin \theta }$